TESTING/LIN/debchvxx.f(3)

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version 3.12.1 · 2 versions
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🎀 NAME 🎀

TESTING/LIN/debchvxx.f — bestie, this is the file this page is about, and it’s chilling in the Library Functions Manual. It’s the home of the debchvxx test subroutine. ✨

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

  • subroutine debchvxx (thresh, path) — DEBCHVXX

💖 Function/Subroutine Documentation 💖

🌸 subroutine debchvxx (double precision thresh, character*3 path)

💫 DEBCHVXX

Purpose: okay so DEBCHVXX will run D**SVXX on a series of Hilbert matrices and then compare the error bounds returned by D**SVXX to see if the returned answer indeed falls within those bounds. 👑

Eight test ratios will be computed. The tests will pass if they are .LT. THRESH. There are two cases that are determined by 1 / (SQRT( N ) * EPS). If that value is .LE. to the component wise reciprocal condition number, it uses the guaranteed case, other wise it uses the unguaranteed case. 🫶

The norm used is the infinity norm. Let Xc be X_computed and Xt be X_truth. Let A be the guaranteed case and B be the unguaranteed case. 💅

Test ratios:

  1. Normwise guaranteed forward error bound.
    • A: both norm ( abs( Xc - Xt ) / norm ( Xt ) .LE. ERRBND( *, nwise_i, bnd_i ) and ERRBND( *, nwise_i, bnd_i ) .LE. MAX(SQRT(N),10) * EPS must hold. If these conditions are met, the test ratio is set to be ERRBND( *, nwise_i, bnd_i ) / MAX(SQRT(N), 10). Otherwise it is 1/EPS.
    • B: For this case, CGESVXX should just return 1. If it is less than one, treat it the same as in 1A. Otherwise it fails. (Set test ratio to ERRBND( *, nwise_i, bnd_i ) * THRESH?)
  2. Componentwise guaranteed forward error bound.
    • A: norm ( abs( Xc(j) - Xt(j) ) ) / norm (Xt(j)) .LE. ERRBND( *, cwise_i, bnd_i ) for all j .AND. ERRBND( *, cwise_i, bnd_i ) .LE. MAX(SQRT(N), 10) * EPS. If these conditions are met, the test ratio is set to be ERRBND( *, cwise_i, bnd_i ) / MAX(SQRT(N), 10). Otherwise it is 1/EPS.
    • B: Same as normwise test ratio.
  3. Backwards error.
    • A: The test ratio is set to BERR/EPS.
    • B: Same test ratio.
  4. Reciprocal condition number.
    • A: A condition number is computed with Xt and compared with the one returned from CGESVXX. Let RCONDc be the RCOND returned by D**SVXX and RCONDt be the RCOND from the truth value. Test ratio is set to MAX(RCONDc/RCONDt, RCONDt/RCONDc).
    • B: Test ratio is set to 1 / (EPS * RCONDc).
  5. Reciprocal normwise condition number.
    • A: The test ratio is set to MAX(ERRBND( *, nwise_i, cond_i ) / NCOND, NCOND / ERRBND( *, nwise_i, cond_i )).
    • B: Test ratio is set to 1 / (EPS * ERRBND( *, nwise_i, cond_i )).
  6. Reciprocal componentwise condition number.
    • A: Test ratio is set to MAX(ERRBND( *, cwise_i, cond_i ) / CCOND, CCOND / ERRBND( *, cwise_i, cond_i )).
    • B: Test ratio is set to 1 / (EPS * ERRBND( *, cwise_i, cond_i )).

Parameters note: from the .. Parameters .. part: NMAX is determined by the largest number in the inverse of the hilbert matrix. Precision is exhausted when the largest entry in it is greater than 2 to the power of the number of bits in the fraction of the data type used plus one, which is 24 for single precision. NMAX should be 6 for single and 11 for double. 🧸

🌟 Author

  • Univ. of Tennessee
  • Univ. of California Berkeley
  • Univ. of Colorado Denver
  • NAG Ltd.

Definition at line 95 of file debchvxx.f.

👑 Author 👑

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💖 cute sign-off: this page is from LAPACK Version 3.12.0, for TESTING/LIN/debchvxx.f(3). Date: not listed on the page. Periodt. 🫶

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